rsync or something else

i want to rsync a file tree to another system. normally this is easy to do with the rsync program. but there a few files (more than one but not all of them) which keep on growing because a program has them open for writing an syncs the metadata so listing them does show new size and time, even if the change is slight. in order to rsync the changes to the target system i must re-run rsync, again. doing rsync, again, is too slow due to startup times. also, there are time periods when none of the files are changed and i want to avoid running rsync more than once in these periods. i do not find any options for rsync to detect a few changing files in the source tree. a duckduckgo search does not find any other program to do this. i can only imagine something with a remote file system as a hack to achieve this. any ideas?